Sensitivity and robust stability of some control systems containinga nonlinear plant

Sufficient conditions for insensitivity and robust stability of some frequently used control systems which contain a nonlinear plant and are not of a feedback type are presented. These conditions are derived from some results of the author (1991) on general input-output systems. They are stated in terms of the transmission operators that describe the blocks constituting the system     

Digital self-triggered robust control of nonlinear systems

In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.     

The control of large-scale nonlinear econometric systems

After pointing out the special characteristics of existing econometric models which form the basis of the application of optimal control techniques for macroeconomic policy analysis and formulation, this paper surveys the use of econometric models for the projection of the economic consequences of alternative policies and the formulation of optimal policies. It presents both the theory and the computational aspects of a particular approach of applying feedback control to study policy options using large-scale nonlinear systems of simultaneous econometric equations. It then illustrates this approach by solving an optimal control problem using the Michigan Quarterly Econometric Model Some topics of further research are suggested in the conclusion.     

-bounded robust control of nonlinear cascade systems

In this paper, we consider the L^∞-bounded robust control problem for a class of nonlinear cascade systems with disturbances. Sufficient conditions are provided under which a hard bound is imposed on the system performance measure. The backstepping approach is used for controller design. A practical example is provided to illustrate the method.     

不确定关联大系统对时变参数的自适应控制

考虑具有时滞的不确定非线性关联大系统的鲁棒控制问题．假设不确定时变参数为半线性或非线性系统的有界输出，通过对时变不确定参数设计自适应律，从而对不确定参数进行估计．利用线性矩阵不等式技术和自适应参数估计方法，设计出鲁棒自适应控制器，从而保证闭环系统渐近稳定．建立了可由线性矩阵不等式表示的镇定条件．仿真示例说明该方法是有效的．     

On robust stability of discrete-time adaptive nonlinear control

We consider adaptive control of discrete-time nonlinear systems with a single unknown parameter in this paper. We demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of Guo [On critical stability of discrete-time adaptive nonlinear control, IEEE Trans. Automat. Control 42 (1997) 1488–1499] which addresses unbounded noise in a stochastic setting. Also in our worst-case approach, we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4.     

On robust stability of interval control systems

The authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty. The basic system considered is that of the classical Lur'e problem of nonlinear control theory. A robust version of the Lur'e problem consisting of a family of linear time-invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector-bounded nonlinear gains is presently treated. By using the Kharitonov theorem to develop some extremal results on positive realness of interval transfer functions (i.e. a family of rational transfer functions with bounded independent coefficient perturbations), the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed. These calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

Decentralized robust disturbance attenuation for a class of large-scale nonlinear systems

We solve the problem of decentralized H_∞ almost disturbance decoupling for a class of large-scale nonlinear uncertain systems in the absence of matching conditions. The method combines ideas from decentralized adaptive control and centralized nonlinear H_∞ control. We relax earlier assumptions on the uncertain time-varying interconnections which are demanded to be only bounded by general nonlinear functions in this work.     

不确定奇异大系统分散鲁棒预测控制

针对一类不确定奇异关联大系统,讨论了当系统状态不可测时,基于输出反馈的分散鲁棒预测控制问题.通过构造Lyapunov函数以及应用线性矩阵不等式方法,将"min-max"优化问题转化为凸优化问题求解,从而得到了输出反馈分散控制器存在的充分条件和显示表达式.证明了优化问题在初始时刻的可行解能保证奇异闭环大系统渐近稳定且正则无脉冲.仿真结果验证了算法的有效性.     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

Nash-based robust distributed model predictive control for large-scale systems

In this paper, a new robust distributed model predictive control (RDMPC) is proposed for large-scale systems with polytopic uncertainties. The time-varying system is first decomposed into several interconnected subsystems. Interactions between subsystems are obtained by a distributed Kalman filter, in which unknown parameters of the system are estimated using local measurements and measurements of neighboring subsystems that are available via a network. Quadratic boundedness is used to guarantee the stability of the closed-loop system. In the MPC algorithm, an output feedback-interaction feedforward control input is computed by an LMI-based optimization problem that minimizes an upper bound on the worst case value of an infinite-horizon objective function. Then, an iterative Nash-based algorithm is presented to achieve the overall optimal solution of the whole system in partially distributed fashion. Finally, the proposed distributed MPC approach is applied to a load frequency control (LFC) problem of a multi-area power network to study the efficiency and applicability of the algorithm in comparison with the centralized, distributed and decentralized MPC schemes.     

Special issue on Learning and control in cooperative multi-agent systems

Guest Editors
Frank L. Lewis UTA Research Institute, The University of Texas at Arlington, Texas, U.S.A.
Zhong-Ping Jiang Department of Electrical and Computer Engineering, Polytechnic Institute of NYU, Brooklyn, NY, U.S.A.     

Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays

This paper addresses the stability problem of fuzzy large-scale systems (FLSSs) with uncertainties and arbitrary time-varying delays. The stability conditions, which are less conservative and more applicable than the existing results, are derived by a novel Lyapunov-Krasovskii functional method and expressed in terms of linear matrix inequalities (LMIs). Two examples are given to demonstrate the correctness and advantage of our theoretical results.